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The Japan international was an integral part of the Dortmund side that won back-to-back Bundesliga titles, prompting a £17 million move to Old Trafford in 2012.

Kagawa struggled to acclimatise in his first season despite contributing towards United’s 20th league title, while injuries allied to a chronic loss of form and confidence saw him restricted to making just 30 appearances in all competitions under David Moyes last season.

After running the rule over his squad in pre-season and the early part of the Premier League campaign Louis van Gaal has deemed Kagawa, who is likely to have made his final United appearance in the embarrassing 4-0 defeat against MK Dons in the Capital One Cup on Tuesday, surplus to requirements.

The Old Trafford giants are looking to trim their squad as a result of their record summer outlay and are willing to listen to offers for the likes of Kagawa and Javier Hernandez, while Danny Welbeck could also depart before the close of the window.

Dortmund, who on Thursday were drawn in the same Champions League group as Arsenal, are keen to take Kagawa on a season-long loan with a view to buy.

Jurgen Klopp’s side finished runners-up to Bayern Munich in the Bundesliga last season and lost key striker Robert Lewandowski to their fiercest rivals earlier this summer.